%2B(2x%5E3%2Bx%5E2-6x-3)-(5x%5E3%2B8x%5E2).jpeg "(1-x+4x^2-8x^3)+(2x^3+x^2-6x-3)-(5x^3+8x^2)")
Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the following polynomial expression:
(1 - x + 4x² - 8x³) + (2x³ + x² - 6x - 3) - (5x³ + 8x²)
Understanding the Steps
To simplify this expression, we need to follow these key steps:
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Remove the parentheses: Pay attention to the signs before each set of parentheses. If there's a plus sign, we can simply remove the parentheses. If there's a minus sign, we need to change the sign of each term inside the parentheses.
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Combine like terms: Identify terms with the same variable and exponent (e.g., x², x³, constant terms) and combine their coefficients.
Simplifying the Expression
Let's apply these steps to our expression:
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Remove the parentheses: (1 - x + 4x² - 8x³) + (2x³ + x² - 6x - 3) - (5x³ + 8x²) = 1 - x + 4x² - 8x³ + 2x³ + x² - 6x - 3 - 5x³ - 8x²
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Combine like terms: -8x³ + 2x³ - 5x³ + 4x² + x² - 8x² - x - 6x + 1 - 3 = -11x³ - 3x² - 7x - 2
The Simplified Expression
Therefore, the simplified form of the polynomial expression (1 - x + 4x² - 8x³) + (2x³ + x² - 6x - 3) - (5x³ + 8x²) is -11x³ - 3x² - 7x - 2.